Bounding back and forth through the complex field

The first seminar will be given with the new students in

mind. It will begin with a brief overview of quantifier elimination and its

relation to the back-and-forth property.I shall then discuss complexity issues

with particular reference to algebraically closed fields.In particular,how much

does the height and degree of polynomials in a formula increase when a

quantifier is eliminated? The precise answer here gave rise to the definition

of a `generic' transcendental entire function,which will also be

discussed.